2
If I am a miner, it makes sense for me to broadcast recent blocks since I want my chain to be the longest (see What encourages Bitcoin miners to relay blocks?).
However, what is my incentive for broadcasting old blocks? Deep blocks are very unlikely to be orphaned, so it seems that I get no gain from relaying them, despite it costing me bandwidth.
2
There is no incentive to serve historical blocks beyond altruism, generally that applies to all facets of participating in the p2p network. Nodes without incoming connections will generally not be requested to send any old blocks, and this is a standard operating mode for people who have disabled listening or are behind restrictive NAT with no ability to hole punch through port 8333.
3
Miners have spent money on mining hardware. The value they are able to get out of that mining hardware is tied directly to the price of Bitcoins and the mining difficulty.
If the price goes up, that will incentivize some additional miners and if the price goes down, more people will mine. But this doesn't happen immediately nor does it cancel out perfectly. Miners benefit from an increase in the price of Bitcoins and are harmed by a drop in the price of Bitcoins.
Your incentive for sending old blocks is that the utility of bitcoins drops if it's more difficult for new nodes to join the network. While this effect on the price of bitcoins is slight, the amount of old blocks you need to send is also slight.
And this is true not only for miners: anyone invested in Bitcoin (for example by owning a few bitcoin) stands to gain from an increase in price. – Jannes – 2015-09-24T18:17:57.147
If one really can't upload old blocks, they can consider running a full node in pruning mode, which actually deletes old blocks from your harddisk as well. It's a bit crude in the current version, but upcoming versions will be quite flexible. – Jannes – 2015-09-24T18:21:39.383
Yes miners have a stake in the health of bitcoin in general, but surely this is a free-rider problem? I don't have to relay any blocks so long as someone else does. – sdgfsdh – 2015-09-24T18:57:08.520
@sdgfsdh The cost of relaying is so low and the benefits so great that there is no free rider problem. – David Schwartz – 2015-09-25T08:27:35.527
Why does there need to be an incentive? I mean, strictly speaking, there's no incentive for the people who operate archive.org to keep that old data around. – Nick ODell – 2015-09-24T16:34:06.353